Average Error: 61.2 → 61.2
Time: 27.4s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\frac{\frac{{\left(\frac{\pi}{2} \cdot \frac{\pi}{2}\right)}^{3} - {\left(\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{3}}{{\left(\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{4} + \frac{\pi}{2} \cdot \left({\left(\frac{\pi}{2}\right)}^{3} + \frac{\pi \cdot {\left(\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{2}}{2}\right)}}{\frac{\pi}{2} + \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]
\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
↓
\frac{\frac{{\left(\frac{\pi}{2} \cdot \frac{\pi}{2}\right)}^{3} - {\left(\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{3}}{{\left(\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{4} + \frac{\pi}{2} \cdot \left({\left(\frac{\pi}{2}\right)}^{3} + \frac{\pi \cdot {\left(\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{2}}{2}\right)}}{\frac{\pi}{2} + \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}
double code(double a) {
	return acos(pow(fmod(cosh(a), (a * a)), log1p(a)));
}
↓
double code(double a) {
	return (((pow(((((double) M_PI) / 2.0) * (((double) M_PI) / 2.0)), 3.0) - pow((asin(pow(fmod(cosh(a), (a * a)), log1p(a))) * asin(pow(fmod(cosh(a), (a * a)), log1p(a)))), 3.0)) / (pow(asin(pow(fmod(cosh(a), pow(a, 2.0)), log1p(a))), 4.0) + ((((double) M_PI) / 2.0) * (pow((((double) M_PI) / 2.0), 3.0) + ((((double) M_PI) * pow(asin(pow(fmod(cosh(a), pow(a, 2.0)), log1p(a))), 2.0)) / 2.0))))) / ((((double) M_PI) / 2.0) + asin(pow(fmod(cosh(a), (a * a)), log1p(a)))));
}

Error

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.2

    \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
  2. Using strategy rm

  3. Applied acos-asin61.2

    \[\leadsto \color{blue}{\frac{\pi}{2} - \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]
  4. Using strategy rm

  5. Applied flip--61.2

    \[\leadsto \color{blue}{\frac{\frac{\pi}{2} \cdot \frac{\pi}{2} - \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}{\frac{\pi}{2} + \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\]
  6. Using strategy rm

  7. Applied flip3--61.2

    \[\leadsto \frac{\color{blue}{\frac{{\left(\frac{\pi}{2} \cdot \frac{\pi}{2}\right)}^{3} - {\left(\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{3}}{\left(\frac{\pi}{2} \cdot \frac{\pi}{2}\right) \cdot \left(\frac{\pi}{2} \cdot \frac{\pi}{2}\right) + \left(\left(\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right) \cdot \left(\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right) + \left(\frac{\pi}{2} \cdot \frac{\pi}{2}\right) \cdot \left(\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)}}}{\frac{\pi}{2} + \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]

  8. Simplified61.2

    \[\leadsto \frac{\frac{{\left(\frac{\pi}{2} \cdot \frac{\pi}{2}\right)}^{3} - {\left(\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{3}}{\color{blue}{{\left(\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{4} + \frac{\pi}{2} \cdot \left({\left(\frac{\pi}{2}\right)}^{3} + \frac{\pi \cdot {\left(\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{2}}{2}\right)}}}{\frac{\pi}{2} + \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]

  9. Final simplification61.2

    \[\leadsto \frac{\frac{{\left(\frac{\pi}{2} \cdot \frac{\pi}{2}\right)}^{3} - {\left(\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{3}}{{\left(\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{4} + \frac{\pi}{2} \cdot \left({\left(\frac{\pi}{2}\right)}^{3} + \frac{\pi \cdot {\left(\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{2}}{2}\right)}}{\frac{\pi}{2} + \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]

Reproduce

herbie shell --seed 2020071 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))